Sampling low-spectrum signals on graphs via cluster-concentrated modes: examples

TL;DR

This paper develops frame inequalities for signals on specific graph families, using localized eigenvectors of spectral operators to analyze low-spectrum signals on clustered graph structures.

Contribution

It introduces a novel approach to sampling low-spectrum signals on graphs through cluster-based localizations of eigenvectors, establishing new frame inequalities.

Findings

Frame inequalities are established for signals on cube-cycle graph combinations.

Localized eigenvector functions serve as effective frame elements.

The method applies to signals in Paley–Wiener spaces on these graphs.

Abstract

We establish frame inequalities for signals in Paley--Wiener spaces on two specific families of graphs consisting of combinations of cubes and cycles. The frame elements are localizations to cubes, regarded as clusters in the graphs, of vertex functions that are eigenvectors of certain spatio--spectral limiting operators on graph signals.